Alexandrov's Patchwork and the Bonnet-Myers Theorem for Lorentzian Length Spaces
Explore global timelike curvature bounds in Lorentzian length spaces, examining Alexandrov's Patchwork analogue and Bonnet-Myers theorem applications for spacetime geometry.
Gromov's Reconstruction Theorem and Measured Gromov-Hausdorff Convergence in Lorentzian Spaces
Explore Lorentzian space convergence, Gromov reconstruction theorem, and measured Lorentz-Gromov-Hausdorff convergence in nonsmooth general relativity. Gain insights into isomorphy of measured Lorentzian spaces.
The Space of Causal Diamonds as a Lorentzian Pre-Length Space
Explore causal diamonds in Mathematical Relativity, examining their geometry and geodesic structure when endowed with Hausdorff distance, and their implications for metric convergence stability.
Properties of the Null Distance on a Spacetime
Explore the null distance concept in spacetime, its definition, examples, and relationship to metric space structures.
Global Hyperbolicity Through the Eyes of the Null Distance
Explore global hyperbolicity in spacetime geometry through null distance, encoding causal information in metric space structures and characterizing completeness.
Constructing Distance Realizers via Midpoints in Lorentzian Mid-Length Space
Explore Lorentzian pre-length spaces, null distance, and midpoint properties to construct distance realizers between timelike related points in non-regular spacetime geometry.
Feynman Propagators on Curved Spacetime
Explore Feynman propagators on curved spacetime, their construction, and connection to quantum states. Delve into microlocal techniques and their application to wave and Dirac-type operators.
Uniqueness and Non-Uniqueness for Percolation on Groups
Explore percolation theory on groups, examining uniqueness and non-uniqueness of infinite clusters and their connections to group-theoretic concepts.
Elements of General Relativity - Lecture 2
Explore advanced concepts in general relativity, focusing on geometry beyond Riemann and examining curvature and rigidity in spacetime.
Elements of General Relativity - Lecture 3
Explore advanced concepts in general relativity, focusing on geometry beyond Riemann and examining curvature and rigidity in spacetime.
A Wilsonian Effective Action for (1+3+6)-Dimensional Emergent Universes in the IKKT Model
Explore the IKKT model's potential for describing Type IIB superstring theory and its emergent universe solutions, focusing on the natural emergence of Lorentz invariant mass terms.
Lorentzian Length Spaces: An Introduction to Synthetic Lorentzian Geometry
Explore synthetic Lorentzian geometry foundations, focusing on time separation functions, curvature bounds, and applications in General Relativity, including recent developments in singularity theorems.
On the Classification Problem for Static Metrics with Positive Cosmological Constant
Explore recent advances in classifying static solutions to vacuum Einstein field equations with positive cosmological constant and related mass concepts in general relativity.
A Quiescent Regime for Big Bang Formation
Explore stable big bang formation in general relativity, covering recent results and a new condition for big bang formation in Einstein-non-linear scalar field settings.
Mathematical General Relativity: Seventy-Two Years After Yvonne Bruhat's Foundational Acta Paper
Explore key achievements in mathematical general relativity since Y.C Bruhat's foundational Acta paper, reviewing 72 years of progress in the field.
Mass Aspect Function for Weakly Regular Asymptotically Hyperbolic Manifolds
Explore mass aspect function definition for weakly regular asymptotically hyperbolic manifolds, extending Wang's work to low regularity settings using cut-off functions and distribution theory.
How Minimal Hypersurface and MOTS Singularities Affect Relativity Theorems
Explore how singularities in minimal hypersurfaces and MOTS impact key theorems in relativity, focusing on challenges and solutions in different dimensions.
Formation of Quiescent Big Bang Singularities
Explore general relativity's big bang singularities, recent stability results, and a new condition for big bang formation in Einstein-non-linear scalar field settings.
Non-Regular Spacetime Geometry via Metric Measure Geometry
Explore non-regular spacetime geometry using metric geometry, extending Lorentzian geometry beyond classical differential geometry for low-regularity spacetimes and general spaces.
Metric Geometry of Spaces of Persistence Diagrams
Explore metric geometry of persistence diagram spaces, focusing on synthetic curvature bounds and applications in non-smooth, infinite-dimensional contexts.
Taxonomy of Infinite Distance Limits in Quantum Gravity Moduli Spaces
Explore geometric classification of light towers in quantum gravity moduli spaces, examining constraints, evidence, and applications in infinite-distance limits.